I play quite a bit of solo-top Fiora. Know how many games I've lost as her? One; three if you count games you lose to teammates DC'ing. How did I manage that kind of W/L ratio? By building her for what she is instead of like a normal solo top. What Fiora is is a walking overpowered R button, and the rest of her kit is merely gravy (particularly GOOD gravy, good to the point where I'd even eat it even though I hate gravy on my food, but gravy nonetheless). My entire build is about maximizing her R for the best balance of single- and multi-target burst. Make no mistake, though. You WILL die with this build. You will die a LOT. If you do this in solo queue, you'll probably get some seriously raging teammates and a few reports. You're there to ult, watch the enemy team ALL drop to half health instantly, then get off a couple of auto-attacks before you drop, which will be immediately. Without further ado...

Runes & Masteries

Runes
-Movement speed Quints
-Armor penetration Marks
-Armor per-level seals
-Magic resist per-level Glyphs
This setup lets you get in the fight quickly (you'll be taking literally every source of movement speed you can get from runes and masteries, which winds up giving a LOT of speed), ignore some enemy armor for your ult, and lets you stay alive *just* long enough to ult. That's all you want.

Masteries
0/21/9. This is not negotiable. Grab the resistances, health, Indomitable, Intiator, one point in Enlightenment, Mercenary, then Juggernaut in defense, the Good Hands, Quickness, and 2 points in Expanded Mind in utility. If you want to move your points around, the best things to lose are Indomitable and the point in Enlightenment. You need everything else. The health/resistances are again to keep you alive just long enough to ult, Initiator lets you get close enough to dash in for it, Mercenary means you actually get good gold returns for these suicide runs, Good Hands let you pop back up a little sooner when you do them, Juggernaut lets you shake off CC that would keep you from ulting sooner, and Quickness for the same reason as Initiator.

skill Order
R>W>Q at level 2>E>Q
(Alternate situational option, see below: R>E>Q at level 2>W>Q)
A common misconception about Fiora is that her E is the strongest part of her kit besides her ult and should be maxed first. You've been lied to. Riposte is probably the best spell for a solo top in human history. The majority of solo tops are either AD, or have a spell that applies to their next autoattack. Riposte lets you not only negate the damage it deals, but also you nuke them for a surprisingly-large chunk of their health in return. Plus, it's also quite a bit of free AD. Use the situational option when they legitimately aren't either AD or have a one-off on-hit effect. One thing to note is you have to get good at recognizing when these things are coming, otherwise maxing Riposte just gives you free AD which is great but your E would at that point be better for you.

Build And spells
spells
Flash and your choice of Exhaust, Ignite, or Teleport.

Build
start: Boots & three potions
Get a Tiamat and a Mercury's Treads as soon as possible. If you get knocked out of lane early, get one of the cheap bits of Tiamat (preferably the health regen). (Yes, TIAMAT. stop laughing, you know you've lost to a Tiamat Fiora at least once.) If you can, stay in lane until you can afford both of them entirely, then buy them all in one go. After that, buy a Bloodthirster, getting the lifesteal first. After your Bloodthirster, you have three options:

1) A second Bloodthirster
2) A second Tiamat
3) A Frozen Mallet

You'll BUILD all of these, but the order doesn't matter. I personally usually go with the Tiamat, then the Mallet, then the BT.

Armor getting you down? Swap one Bloodthirster with a Last Whisper. Suddenly, no armor problems!

Now, you may be asking "But isn't Tiamat a bad item?" Normally you'd be right. But this is Fiora. Her ult applies ALL on-hit effects. Five times. Tiamat gives you 50% splash damage, that stacks per Tiamat you have. With two Tiamats, every hit of your ult does just as much damage to everything near the target as well as the target. (If you have three or more Tiamats, it now does MORE damage to those nearby, but even I have to admit that there's a point where you've gone into excess.) Tiamat also provides quite a bit of AD, and amazing early-game stats, all at a VERY competitive price. (Fun fact: Tiamat is actually proven to be one of the most gold-efficient items in terms of pure stats in the game.) Fiora actually isn't terribly strong early game, and the health and mana regen are quite welcome during your early laning.

You may also be asking: "Why Mallet?" Well, when you proc Tiamat, you also apply any non-Tiamat on-hit effects to everything in your splash AoE, Mallet included. Five AoE slows is just too good to pass up, plus it provides a little always-welcome AD, and some health that by the time in the game you'll be building it you'll really want so as to not melt before you can ult.

And I KNOW you're NOT asking "Why Bloodthirster?" because that would mean you're really, really dumb.

strategy
Laning
Your goal in laning is to farm and not die. That's it. If the enemy top tries to get on you, you Riposte their attack, autoattack them ONCE, then walk away. If they insist on fighting, you turn on your E, and give 'em hell. Once your E wears off, you resume walking away. If you win the trade and they start running, you walk away and resume farming. You do NOT chase past the river unless you will immediately get a kill. You will be doing plenty of dying later, don't get an early start on it.

When ganked, the best thing you can do is attempt to juke them out by using your Q to jump to an enemy minion behind them, then (if you're on blue team) run down the tri-bush and through the jungle on purple side as far as it takes to lose them. You're really, really fast during early levels, so this typically works. If the enemy mid tries to jump on you, Q to them, then if possible, Q to a minion in mid. Your goal is simply to survive the gank and make them waste time chasing you. If you're on purple team, the best you can do when ganked is Q to a caster minion, juke into the bush, then Q back to an enemy melee minion when they chase you. Also, be liberal with your Flash for escaping during laning. Alive with no Flash is better than dead.

Team fights
Your goal in team fighting is very single-minded:

YOU WANT TO ULT ON A BUNCH OF PEOPLE.

That's it. You want to wait until there are two or three enemy players within Tiamat range of each other, then ult. If you get caught and are guaranteed dead, you ult. You don't care about getting kills, or surviving (although if you can manage it, surviving is nice. Ulting>surviving, however. Think Karthus.). Why don't you care about kills? Because one ult on this build reliably gets all high value targets so low than they either have to retreat or die, so your team just cleans up.* If you don't immediately die post-ult, just leave and only come back when all that's left is clean-up of the low-value targets.






And last of all...

Happy Fiora-ing! May all your ult-grenades be teamfight-winning!

*Disclaimer: Only do this build if you're confident that your teammates have enough firing synapses to clean up. Otherwise, you're wasting your time.